Abstract: We study the dynamics of an electron wave-packet in a two-dimensional squarelattice with an aperiodic site potential in the presence of an external uniformelectric field. The aperiodicity is described by $\epsilon {\bf m} =V\cos{\pi\alpha m x^{ u x}}\cos{\pi\alpha m y^{ u y}}$ at lattice sites$m x, m y$, with $\pi \alpha$ being a rational number, and $ u x$ and$ u y$ tunable parameters, controlling the aperiodicity. Using an exactdiagonalization procedure and a finite-size scaling analysis, we show that inthe weakly aperiodic regime $ u x, u y < 1$, a phase of extended statesemerges in the center of the band at zero field giving support to a macroscopicconductivity in the thermodynamic limit. Turning on the field gives rise toBloch oscillations of the electron wave-packet. The spectral density of theseoscillations may display a double peak structure signaling the spatialanisotropy of the potential landscape. The frequency of the oscillations can beunderstood using a semi-classical approach.